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Bayesian sensitivity analysis with the Fisher–Rao metric

Kurtek, Sebastian; Bharath, Karthik

Authors

Sebastian Kurtek



Abstract

We propose a geometric framework to assess sensitivity of Bayesian procedures to modelling assumptions based on the nonparametric Fisher–Rao metric. While the framework is general, the focus of this article is on assessing local and global robustness in Bayesian procedures with respect to perturbations of the likelihood and prior, and on the identification of influential observations. The approach is based on a square-root representation of densities, which enables analytical computation of geodesic paths and distances, facilitating the definition of naturally calibrated local and global discrepancy measures. An important feature of our approach is the definition of a geometric ϵ-contamination class of sampling distributions and priors via intrinsic analysis on the space of probability density functions. We demonstrate the applicability of our framework to generalized mixed-effects models and to directional and shape data.

Citation

Kurtek, S., & Bharath, K. (2015). Bayesian sensitivity analysis with the Fisher–Rao metric. Biometrika, 102(3), https://doi.org/10.1093/biomet/asv026

Journal Article Type Article
Acceptance Date Mar 12, 2015
Publication Date Jul 15, 2015
Deposit Date Feb 27, 2017
Publicly Available Date Feb 27, 2017
Journal Biometrika
Print ISSN 0006-3444
Electronic ISSN 0006-3444
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 102
Issue 3
DOI https://doi.org/10.1093/biomet/asv026
Keywords Fisher–Rao metric, Geodesic, Geometric ϵ-contamination, Influence analysis, Riemannian manifold
Public URL http://eprints.nottingham.ac.uk/id/eprint/40807
Publisher URL https://academic.oup.com/biomet/article-lookup/doi/10.1093/biomet/asv026
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information This is a pre-copyedited, author-produced version of an article accepted for publication in Biometrika following peer review. The version of record Bayesian sensitivity analysis with the Fisher–Rao metric
Biometrika (2015) 102 (3): 601-616 is available online at: https://academic.oup.com/biomet/article-lookup/doi/10.1093/biomet/asv026

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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